Finite Group Databasebeta

← #12102760

Subgroups — #12102760

Order 1280.

1026 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65169C211yesmaximal, characteristic
2C2×#65149C211yesmaximal, characteristic
3C2×D5×C4⋊C8C211yesmaximal, characteristic
4#10605879C211yesmaximal, characteristic
5C4×#4038C211yesmaximal, characteristic
6C5×#1949C211yesmaximal, characteristic, complemented
7#10601408C211yesmaximal, characteristic, complemented
8#10601356C211yesmaximal, characteristic, complemented
9#10601248C211yesmaximal, characteristic, complemented
10#10600333C211yesmaximal, characteristic, complemented
11#10600261C211yesmaximal, characteristic, complemented
12#10599659C211yesmaximal, characteristic
13#10599659C211yesmaximal, characteristic
14#10599589C211yesmaximal, characteristic, complemented
15#10599588C211yesmaximal, characteristic, complemented
16C22×C8×D5C2211yescharacteristic
17C22×C8×D5C2211yescharacteristic
18C2×#4038C2211yescharacteristic
19C2×#4038C2211yescharacteristic
20C2×#4038C2211yescharacteristic
21C2×#4038C2211yescharacteristic
22C2×C42×D5C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C5×#382C2211yescharacteristic
27C4×C5×C4⋊C4C2211yescharacteristic
28C2×#3950C2211yescharacteristic
29C2×#3949C2211yescharacteristic
30C2×#3946C2211yescharacteristic
31C2×#3946C2211yescharacteristic
32#65265C2211yescharacteristic
33#65265C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C4×#685—21no—
41#65225C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43C42×Dic5—21no—
44C2×C4⋊#168C2211yescharacteristic
45#65169—24no—
46#65149—24no—
47D5×C4⋊C8C418yescomplemented
48#64956—21no—
49#64956—21no—
50#64955—21no—
51#64938—21no—
52#64938—21no—
53#64937—21no—
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56#64771C2211yescharacteristic
57#64771C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#64749C2211yescharacteristic
61#64749C2211yescharacteristic
62#21169—51nomaximal, Sylow
63C22×C4×D5D411yescharacteristic
64C22×C4×D5D411yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C42×C5—21no—
73C2×C42×C5C2311yescharacteristic
74C2×#685—21no—
75C2×#685—21no—
76C2×#685—21no—
77C2×#685—21no—
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×C4⋊Dic5C2311yescharacteristic
82C2×#683—21no—
83C2×#683—21no—
84C2×#683—21no—
85C2×#683—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5—21no—
88C2×C4×Dic5—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5D411yescharacteristic
94C2×C4×Dic5D411yescharacteristic
95C2×C4×Dic5C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C2×C8×D5—22no—
99C2×C8×D5—22no—
100C2×C8×D5—22no—
101C2×C8×D5—22no—
102C2×C8×D5C2×C414yes—
103C2×C8×D5C2×C414yes—
104#4038—22no—
105#4038—22no—
106#4038—22no—
107#4038—22no—
108#4038—22no—
109#4038—22no—
110#4038D414yes—
111#4038Q814yes—
112C42×D5C2×C414yes—
113C42×D5Q814yes—
114C5×#107—22no—
115C5×#106—22no—
116C5×C4⋊C8C2×C414yes—
117C5×#95—21no—
118C5×#95—21no—
119C5×#95—21no—
120#3963—21no—
121#3963—21no—
122#3963—21no—
123#3963—21no—
124#3963—21no—
125#3950—22no—
126#3949—22no—
127#3946C2×C414yes—
128#3946C2×C414yes—
129#3940—22no—
130#3940—22no—
131#3939—22no—
132#3939—22no—
133C4⋊#168C2×C414yes—
134C2×#427—51no—
135C2×#427—51no—
136C22×C4⋊C8—51no—
137#2285—51no—
138C4×#117—51no—
139#1949—51no—
140#1949—51no—
141#1949—51no—
142#1949D511yescharacteristic, complemented
143#1948—51no—
144#1948—51no—
145#1947—51no—
146#1947—51no—
147#1735—51no—
148#1735—51no—
149C23×D5C2×D411yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2411yescharacteristic
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5C2×D411yescharacteristic
162C22×Dic5C2×D411yescharacteristic
163C22×Dic5C2×D411yescharacteristic
164C2×C4×D5—22no—
165C2×C4×D5—22no—
166C2×C4×D5—41no—
167C2×C4×D5—41no—
168C2×C4×D5C4⋊C414yes—
169C2×C4×D5C4⋊C414yes—
170C2×C4×D5C22×C412yes—
171C2×C4×D5C2×D412yes—
172C2×C4×D5C2×Q812yes—
173C2×C4×D5C2×Q812yes—
174C2×C4×D5#4112yes—
175C2×C4×D5#4112yes—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8C22×C412yes—
181C2×C5×C8C22×C412yes—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4C2×D412yes—
189C5×C4⋊C4C2×Q812yes—
190C42×C5—42no—
191C42×C5C22×C412yes—
192C42×C5C2×Q812yes—
193#685—24no—
194#685—24no—
195#685—42no—
196#685—42no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5C2×D412yes—
204C4⋊Dic5C2×Q812yes—
205#683—42no—
206#683—42no—
207#683—42no—
208#683—42no—
209C4×Dic5—24no—
210C4×Dic5—24no—
211C4×Dic5—42no—
212C4×Dic5—42no—
213C4×Dic5—42no—
214C4×Dic5—42no—
215C4×Dic5—42no—
216C4×Dic5C4⋊C414yes—
217C4×Dic5C4⋊C414yes—
218C4×Dic5C22×C412yes—
219C4×Dic5C2×Q812yes—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168C22×C412yes—
225C2×#168C22×C412yes—
226C8×D5—28no—
227C8×D5—28no—
228C23×C8—51no—
229C23×C8—51no—
230C2×#117—51no—
231C2×#117—51no—
232C2×#117—51no—
233C2×#117—51no—
234C22×C42—51no—
235#427—104no—
236#427—104no—
237C2×#107—51no—
238C2×#107—51no—
239C2×#107—51no—
240C2×#107C2×D511yescharacteristic
241C2×#106—51no—
242C2×#106—51no—
243C2×#106—51no—
244C2×#106C2×D511yescharacteristic
245C2×C4⋊C8—51no—
246C2×C4⋊C8—51no—
247C2×C4⋊C8—51no—
248C2×C4⋊C8—58no—
249C2×C4⋊C8C2×D511yescharacteristic
250#384—51no—
251#384—51no—
252#382—51no—
253#382C2×D511yescharacteristic
254#380—101no—
255#380—101no—
256C4×C4⋊C4—51no—
257C4×C4⋊C4—51no—
258C4×C4⋊C4—51no—
259C4×C4⋊C4—101no—
260C4×C4⋊C4—101no—
261C4×C4⋊C4C2×D511yescharacteristic
262C4×C22⋊C4—101no—
263C4×C22⋊C4—101no—
264#376—101no—
265C43—101no—
266#340—51no—
267#340—51no—
268#340—51no—
269#340—51no—
270#340—51no—
271#340—51no—
272#340C2×D511yescharacteristic
273#340C2×D511yescharacteristic
274C23×C5C22×D411yescharacteristic
275C22×D5—21no—
276C22×D5—21no—
277C22×D5—21no—
278C22×D5—21no—
279C22×D5C2×C4⋊C412yes—
280C22×D5#12112yes—
281C22×D5C22⋊Q812yes—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5C2×C4⋊C412yes—
299C2×C4×C5C2×C4⋊C412yes—
300C2×C4×C5C23×C411yescharacteristic
301C2×C4×C5C22×D411yescharacteristic
302C2×C4×C5C22×Q811yescharacteristic
303C2×C4×C5C22×Q811yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5C2×C4⋊C412yes—
321C2×Dic5C2×C4⋊C412yes—
322C2×Dic5C2×C4⋊C412yes—
323C2×Dic5#12112yes—
324C2×Dic5C22⋊Q812yes—
325C2×Dic5#13512yes—
326C2×Dic5#13512yes—
327C4×D5—28no—
328C4×D5—44no—
329C4×D5C4×D414yes—
330C4×D5C4×Q814yes—
331C4×D5#12514yes—
332C4×D5C4⋊Q814yes—
333C5×C8—22no—
334C5×C8—22no—
335#168—22no—
336#168—22no—
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C22×C8—51no—
341C22×C8—51no—
342C22×C8—54no—
343C22×C8—54no—
344C22×C8—102no—
345C22×C8—102no—
346C22×C8—102no—
347C22×C8—102no—
348C22×C8C22×D511yescharacteristic
349C22×C8C22×D511yescharacteristic
350#117—54no—
351#117—54no—
352#117—102no—
353#117—102no—
354#117—102no—
355#117—102no—
356#117—102no—
357#117—102no—
358C2×C4⋊C4—51no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—101no—
364C2×C4⋊C4—101no—
365C2×C4⋊C4—101no—
366C2×C4⋊C4C22×D511yescharacteristic
367C2×C4⋊C4C22×D511yescharacteristic
368C2×C4⋊C4C22×D511yescharacteristic
369C2×C4⋊C4C22×D511yescharacteristic
370C2×C22⋊C4—101no—
371C2×C22⋊C4—101no—
372C2×C22⋊C4—101no—
373C2×C22⋊C4—101no—
374C2×C42—21no—
375C2×C42—51no—
376C2×C42—51no—
377C2×C42—51no—
378C2×C42—54no—
379C2×C42—54no—
380C2×C42—101no—
381C2×C42—101no—
382C2×C42—101no—
383C2×C42—101no—
384C2×C42—101no—
385C2×C42—101no—
386C2×C42—101no—
387C2×C42C22×D511yescharacteristic
388#107—22no—
389#107—102no—
390#107—102no—
391#107—102no—
392#106—22no—
393#106—102no—
394#106—102no—
395#106—102no—
396C4⋊C8—54no—
397C4⋊C8—54no—
398C4⋊C8—54no—
399C4⋊C8C4×D514yes—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—101no—
404#95—101no—
405#95—101no—
406#95—101no—
407#95—101no—
408C22×C5C22×C4⋊C411yescharacteristic
409C22×C5C2×#12111yescharacteristic
410C22×C5C2×C22⋊Q811yescharacteristic
411C22×C5C2×#13511yescharacteristic
412C22×C5C2×#13511yescharacteristic
413C22×C5#57511yescharacteristic
414C22×C5#57511yescharacteristic
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—22no—
421C2×D5#38914yes—
422C4×C5—22no—
423C4×C5—22no—
424C4×C5—42no—
425C4×C5—42no—
426C4×C5—81no—
427C4×C5—81no—
428C4×C5C2×C4×D411yescharacteristic
429C4×C5C2×C4×Q811yescharacteristic
430C4×C5C2×#12511yescharacteristic
431C4×C5C2×C4⋊Q811yescharacteristic
432Dic5—22no—
433Dic5—42no—
434Dic5—42no—
435Dic5—81no—
436Dic5—81no—
437Dic5#38914yes—
438Dic5#42714yescomplemented
439C24—51no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—52no—
450C22×C4—52no—
451C22×C4—52no—
452C22×C4—51no—
453C22×C4—54no—
454C22×C4—54no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—101no—
460C22×C4—101no—
461C22×C4—201no—
462C22×C4—201no—
463C22×C4D4×D511yescharacteristic
464C22×C4D4×D511yescharacteristic
465C22×C4C23×D511yescharacteristic
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—52no—
471C2×C8—52no—
472C2×C8—108no—
473C2×C8—108no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8C2×C4×D512yes—
479C2×C8C2×C4×D512yes—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—52no—
487C4⋊C4—52no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4—101no—
494C4⋊C4—202no—
495C4⋊C4—202no—
496C4⋊C4—202no—
497C4⋊C4—202no—
498C4⋊C4D4×D512yes—
499C4⋊C4Q8×D512yes—
500C22⋊C4—104no—
501C22⋊C4—104no—
502C22⋊C4—202no—
503C22⋊C4—202no—
504C42—42no—
505C42—52no—
506C42—52no—
507C42—54no—
508C42—54no—
509C42—104no—
510C42—104no—
511C42—202no—
512C42—202no—
513C42—202no—
514C42—202no—
515C42—202no—
516C42C2×C4×D512yes—
517C42Q8×D512yes—
518C2×C5C2×#38911yescharacteristic
519C2×C5C2×#42711yescharacteristic
520C2×C5#291111yescharacteristic
521C2×C5#303511yescharacteristic
522C2×C5#303511yescharacteristic
523C2×C5#307611yescharacteristic
524C2×C5#307611yescharacteristic
525D5—24no—
526C23—52no—
527C23—52no—
528C23—52no—
529C23—101no—
530C23—101no—
531C23—101no—
532C23—101no—
533C23C2×D4×D511yescharacteristic
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—52no—
551C2×C4—52no—
552C2×C4—52no—
553C2×C4—52no—
554C2×C4—52no—
555C2×C4—52no—
556C2×C4—54no—
557C2×C4—54no—
558C2×C4—54no—
559C2×C4—54no—
560C2×C4—52no—
561C2×C4—108no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—102no—
565C2×C4—102no—
566C2×C4—204no—
567C2×C4—201no—
568C2×C4—201no—
569C2×C4—201no—
570C2×C4—201no—
571C2×C4—201no—
572C2×C4—201no—
573C2×C4—201no—
574C2×C4—201no—
575C2×C4—201no—
576C2×C4—201no—
577C2×C4D5×C4⋊C412yes—
578C2×C4D5×C4⋊C412yes—
579C2×C4C22×C4×D511yescharacteristic
580C2×C4C2×D4×D511yescharacteristic
581C2×C4C2×Q8×D511yescharacteristic
582C2×C4C2×Q8×D511yescharacteristic
583C2×C4D5×#4111yescharacteristic
584C2×C4D5×#4111yescharacteristic
585C8—22no—
586C8—22no—
587C8—102no—
588C8—102no—
589C5#2116911yescharacteristic, complemented, Sylow
590C22—54no—
591C22—102no—
592C22—102no—
593C22—102no—
594C22—102no—
595C22—102no—
596C22—102no—
597C22C2×D5×C4⋊C411yescharacteristic
598C22D5×#12111yescharacteristic
599C22D5×C22⋊Q811yescharacteristic
600C22D5×#13511yescharacteristic
601C22D5×#13511yescharacteristic
602C22#6610711yescharacteristic
603C22#6611111yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—54no—
609C4—54no—
610C4—81no—
611C4—81no—
612C4—102no—
613C4—202no—
614C4—202no—
615C4—401no—
616C4—401no—
617C4C4×D4×D511yescharacteristic
618C4C4×Q8×D511yescharacteristic
619C4D5×#12511yescharacteristic
620C4D5×C4⋊Q811yescharacteristic
621C2—104no—
622C2D5×#38911yescharacteristic
623C2D5×#42711yescharacteristic
624C2#1061093911yescharacteristic
625C2#1061226411yescharacteristic
626C2#1061232811yescharacteristic
627C2#1061289611yescharacteristic
628C2#1061296011yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1949C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1949D5
hypocenterC5#21169
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. C5×#1949C2semidirect
7. #10601408C2semidirect
8. #10601356C2semidirect
9. #10601248C2semidirect
10. #10600333C2semidirect
11. #10600261C2semidirect
14. #10599589C2semidirect
15. #10599588C2semidirect
47. D5×C4⋊C8C4semidirect
142. #1949D5semidirect
438. Dic5#427semidirect
589. C5#21169semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#651692
C2×#651492
C2×D5×C4⋊C82
#106058792
C4×#40382
C5×#19492
#106014082
#106013562
#106012482
#106003332
#106002612
#105996592
#105995892
#105995882
#211695